Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+2y &= -2 \\ 3x+5y &= 6\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $3x = -5y+6$ Divide both sides by $3$ to isolate $x$ $x = {-\dfrac{5}{3}y + 2}$ Substitute this expression for $x$ in the first equation. $4({-\dfrac{5}{3}y + 2}) + 2y = -2$ $-\dfrac{20}{3}y + 8 + 2y = -2$ Simplify by combining terms, then solve for $y$ $-\dfrac{14}{3}y + 8 = -2$ $-\dfrac{14}{3}y = -10$ $y = \dfrac{15}{7}$ Substitute $\dfrac{15}{7}$ for $y$ in the top equation. $4x+2( \dfrac{15}{7}) = -2$ $4x+\dfrac{30}{7} = -2$ $4x = -\dfrac{44}{7}$ $x = -\dfrac{11}{7}$ The solution is $\enspace x = -\dfrac{11}{7}, \enspace y = \dfrac{15}{7}$.